1. Planetary albedo (a) is the average reflectivity of the Earth = 107/342  0.3
Earth’s global, annual mean energy balance

2. Earth’s global, annual mean energy balance
Atmosphere:
Total = ( ) W m‑2 - ( ) W m‑2 = 0 W m‑2
Outer Space:
Total = ( ) W m‑ W m‑2 = 0 W m‑2
Surface:
Total = ( ) W m‑2 - ( ) W m‑2 = 0 W m‑2
Greenhouse effect
Earth’s global, annual mean energy balance

3. Earth’s global, annual mean energy balance
T = 255 K
T = 288 K
Greenhouse effect
Earth’s global, annual mean energy balance

4. The numbers represent estimates of each individual energy flux whose uncertainty is given in the parentheses using smaller fonts. Figure from Hartmann et al. (2014) which is adapted from Wild et al. (2013). (Fig. 2.19, Goosse, 2015)

5. Greenhouse Effect A = 4p r2 A = p r2 r a Sun Ts S0 = 1361 W m-2
Emission = sTe4 a
a = planetary albedo (0.30) r
S0 = 1361 W m-2
Sun Ts
Earth

6. Greenhouse Effect (Tech Box 1.4) Global Energy Balance
Incoming Energy = Outgoing Energy
pr2 S0 (1-a) = 4pr2 sTe4
r = radius of Earth
S0 = solar constant (1361 W/m2)
a = planetary albedo (0.30)
s = Stefan-Boltzmann constant
(5.67 x 108 W m-2 K-4)
Te = effective temperature of the Earth
Ts = observed global average surface temperature
Greenhouse Effect
Ts = 288 K
Te = 255 K
33 K (33C° = 59F°)
(Tech Box 1.4)

7. Sensible and latent heat
S0 = “solar constant” = 1361 W/m2
a = planetary albedo = 0.30
Te = effective temperature
Ts = surface temperature
Greenhouse gases
Greenhouse Effect
sTs4
sTe4
Ts = 288K = 15°C (Observed)
Sensible and latent heat
esTe4
Greenhouse Effect
sTe4
Ts = Te = 255K = -18°C

8. The heat balance at the top of the atmosphere
Greenhouse effect
The atmosphere is nearly transparent to visible light.
The atmosphere is almost opaque across most of the infrared part of the electromagnetic spectrum because of some minor constituents (water vapour, carbon dioxide, methane and ozone).
Heat balance of the Earth with an atmosphere represented by a single layer totally transparent to solar radiation and opaque to infrared radiations.

9. The heat balance at the top of the atmosphere
Greenhouse effect
Representing the atmosphere by a single homogenous layer of temperature Ta, totally transparent to the solar radiation and totally opaque to the infrared radiations emitted by the Earth’s surface, the heat balance at the top of the atmosphere is:
The heat balance at the surface is:
This leads to:
This corresponds to a surface temperature of 303K (30°C).

10. The heat balance at the top of the atmosphere
Greenhouse effect
A more precise estimate of the radiative balance of the Earth, requires to take into account
the multiple absorption by the various atmospheric layers and emission at a lower intensity as the temperature decreases with height.
the strong absorption only in some specific ranges of frequencies which are characteristic of each component.
Furthermore, the contribution of non-radiative exchanges have to be included to close the surface energy balance.

11. Present-day insolation at the top of the atmosphere
The irradiance at the top of the atmosphere is a function of the Earth-Sun distance.
Total energy emitted by the Sun at a distance rm= Total energy emitted by the Sun at a distance r
Earth Sr r S0 rm
Sun

12. Present-day insolation at the top of the atmosphere
The Sun-Earth distance can be computed as a function of the position of the Earth on its elliptic orbit :
v is the true anomaly, a, half of the major axis, and ecc the eccentricity.
Schematic representation of the Earth’s orbit around the Sun. The eccentricity has been strongly amplified for the clarity of the drawing.

13. Present-day insolation at the top of the atmosphere
The insolation on a unit horizontal surface at the top of the atmosphere (Sh) is proportional to the angle between the solar rays and the vertical.
energy crossing A1 =energy reaching A2 Sr A1 Sh
qs is the solar zenith angle

14. Present-day insolation at the top of the atmosphere
The solar zenith distance depends on the obliquity.
The obliquity, eobl , is the angle between the ecliptic plane and the celestial equatorial plane.
The obliquity is at the origin of the seasons.
Representation of the ecliptic and the obliquity eobl in a geocentric system.
Presently
eobl =23°27’

15. Present-day insolation at the top of the atmosphere
The solar zenith distance depends on the position (true longitude lt) relative to the vernal equinox.
The vernal equinox corresponds to the intersection of the ecliptic plane with the celestial equator when the Sun “apparently” moves from the austral to the boreal hemisphere.
Representation of the true longitudes and the seasons in the ecliptic plane.

16. Present-day insolation at the top of the atmosphere
The solar zenith distance depends on the latitude (f ) and on the hour of the day (HA, the hour angle).
d is the solar declination. It is related to the true longitude or alternatively to the day of the year.
Those formulas can be used to compute the instantaneous insolation, the time of sunrise, of sunset as well as the daily mean insolation.

17. Present-day insolation at the top of the atmosphere
Daily mean insolation on an horizontal surface (W m-2).
Polar night

18. Hess, Seymour, 1959: Introduction to Theoretical Meteorology
1 W/m2 = ly/day
Hess, Seymour, 1959: Introduction to Theoretical Meteorology

19. Hess, Seymour, 1959: Introduction to Theoretical Meteorology
1 W/m2 = ly/day
Hess, Seymour, 1959: Introduction to Theoretical Meteorology

20. Annual mean net solar flux at the top of the atmosphere (Wm-2)
Radiative balance at the top of the atmosphere
Geographical distribution
Annual mean net solar flux at the top of the atmosphere (Wm-2)
It is a function of the insolation and of the albedo.

21. Radiative balance at the top of the atmosphere
Geographical distribution
Net annual mean outgoing longwave flux at the top of the atmosphere (Wm-2)
It is a function of the temperature and of the properties of the atmosphere.

22. Radiative balance at the top of the atmosphere
Zonal mean of the absorbed solar radiation and the outgoing longwave radiation at the top of the atmosphere in annual mean (in W/m2).
net excess in the radiative flux
net deficit in the radiative flux